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A357522 Reverse run lengths in binary expansions of terms of A063037: for n >= 0, a(n) is the unique k such that A063037(1+k) = A056539(A063037(1+n)).

%I A357522 #12 Oct 03 2022 14:55:27
%S A357522 0,1,2,3,6,5,4,7,8,11,10,9,16,17,18,15,12,13,14,19,32,23,22,21,24,31,
%T A357522 28,27,26,29,30,25,20,33,42,49,48,43,44,47,50,41,34,37,38,53,52,39,36,
%U A357522 35,40,51,46,45,74,75,84,65,58,59,64,85,86,63,60,57,66,83
%N A357522 Reverse run lengths in binary expansions of terms of A063037: for n >= 0, a(n) is the unique k such that A063037(1+k) = A056539(A063037(1+n)).
%C A357522 This sequence is a self-inverse permutation of the nonnegative integers.
%H A357522 Rémy Sigrist, <a href="/A357522/b357522.txt">Table of n, a(n) for n = 0..10944</a>
%H A357522 Rémy Sigrist, <a href="/A357522/a357522.gp.txt">PARI program</a>
%H A357522 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A357522 a(n) = n iff n = 0 or A044813(1+n) belongs to A044918.
%e A357522 For n = 42:
%e A357522 - A063037(1+42) = 86,
%e A357522 - the binary expansion of 86 is "1010110",
%e A357522 - reversing run lengths yields "1001010",
%e A357522 - this corresponds to 74 = A063037(1+34),
%e A357522 - hence a(42) = 34.
%o A357522 (PARI) See Links section.
%Y A357522 See A357523 for a similar sequence.
%Y A357522 Cf. A044918, A056539, A063037.
%K A357522 nonn,look,base
%O A357522 0,3
%A A357522 _Rémy Sigrist_, Oct 02 2022